Polarization of electromagnetic waves.
For EMW propagating in any medium, there is the concept of polarization. EMW polarization is an order in the orientation of the electric and magnetic field strength vectors in a plane perpendicular to the EMW propagation velocity vector. There are elliptical, circular and linear polarizations.
The nature of the polarization is determined by the design and orientation of the transmitting antenna. In the case of linear polarization, the vector E, changing periodically, remains perpendicular to itself during propagation. An antenna in the form of a vertical vibrator radiates a vertical linearly polarized wave. For lossless reception, the vibrator of the receiving antenna must also be oriented vertically.
To create a horizontal linearly polarized wave, the transmitting antenna vibrators must be horizontal. However, for satellite communications, radio waves in the process of propagation penetrate the ionosphere located in the Earth's magnetic field. As a result, the plane of polarization of a linearly polarized wave rotates (the Faraday effect).
The ionosphere turns out to be a medium with birefringence, and the radio wave propagating through it is split into two components. These components propagate in the ionosphere with different phase velocities. Therefore, when passing a certain distance between them, a phase shift appears, which leads to a rotation of the polarization plane. As a result of the mismatch between the polarization of the wave arriving at the receiving point and the polarization of the receiving antenna, energy is lost - polarization fading occurs. To prevent fading, it is necessary to use antennas with circular polarization, in which the vector E rotates at the frequency of the radio wave, describing a helix during propagation. In this case, the value of the vector E will remain constant. On a path equal to the wavelength, the vector E rotates 360 degrees.
To create an antenna with circular polarization, it is necessary to have two transmitting vibrators, offset in space by 90 degrees one relative to the other. They must be fed with currents of equal amplitude with a phase shift of 90 degrees.
Radio waves with circular polarization are emitted, for example, by a turnstile antenna. Reception of waves with circular polarization is possible both on the same type (turnstile, spiral) antennas, and on conventional vibrators
Depending on the direction of rotation of the vector E, circular polarization can be:
- · left-handed;
- right screw.
In the considered example of a linearly polarized wave, it was assumed that the vector at all points is directed parallel or antiparallel to the axis x(see fig. 1.7). In the general case, for a plane harmonic wave propagating along the axis z, both components are nonzero E x and E y, and the electric field vector has the form
where , are unit vectors directed along the axes Ox,Oy Cartesian coordinate system.
Consider a wave whose electric field components change according to the harmonic law
where - phase shift between oscillations.
Let us find the equation of the trajectory along which the end of the vector moves in the plane z = const. Let's rewrite in the form
and with the help we eliminate from this equality cos ( t–kz) and sin ( t–kz):
Recall that the amplitudes E 10 and E 20 is assumed to be a positive number. We transfer the first term of the right side to the left side, divide both sides by E 20 and square them.
We open the brackets and bring the equation to the form
The ratio is the equation of a conic section. The section has the shape of an ellipse, since the corresponding determinant is non-negative, i.e.
An ellipse is inscribed in a rectangle with sides of length 2 E 10 and 2 E 10 (Fig. 1.8). It touches the sides of the rectangle at points AA ( E 10, E 20 cos ) and BB ( E 10 cos , E 20).
So, in the general case, when a plane monochromatic light wave propagates, the end of the vector in the plane z= const describes an ellipse. The magnetic field strength vector behaves similarly. Such a wave is called elliptically polarized.
Imagine the electric field of such a wave at a fixed t it is possible as follows: a helix is drawn on the surface of a straight elliptical cylinder, the beginnings of all vectors are at points of the axis of the cylinder, the ends are on the helix, and the vector itself is everywhere perpendicular to the axis.
Right and left elliptical polarizations
Moving along an ellipse in a plane z= const, the end of the vector can be rotated clockwise or counterclockwise. In order to distinguish between these two states, the concepts are introduced in optics right polarization (for an observer looking towards the light beam, the rotation occurs clockwise) and left polarization (vector rotation in the opposite direction). Let us show that the direction of rotation of the vector depends on the sign of the phase difference . Let's choose a moment in time t 0 , for which t 0 –kz= 0. At this moment, according to the formulas and,
It can be seen from the formula that at the moment when the end of the vector reaches the rightmost point of its trajectory (Fig. 1.8), we have dE y /dt < 0, если 0 < < , and dE y /dt> 0 if - < < 0. Очевидно, что первый из этих случаев соответствует право поляризованной волне, а второй - лево поляризованной.
So, in the general case, a plane monochromatic wave has right or left elliptical polarization. The complete characterization of the polarization ellipse is given by three parameters E 10 ,E 20 and . And, as can be seen from Fig. 1.8, the axes of the ellipse may not be parallel to the axes Ox and Oy. However, if given E 10 ,E 20 and phase difference relating to an arbitrary position of the axes, and if (0 < /2) - angle determined by the ratio
then the principal semiaxes of the ellipse a and b and angle , which the major axis forms with the axis Ox, are found from the formulas
where ( ) is an auxiliary angle that determines the shape and orientation of the oscillation ellipse, namely:
Numerical value tg determines the ratio of the axes of the ellipse, and the sign at characterizes two options that can be used when describing an ellipse. It can be seen from the last formula that for the right elliptical polarization, when sin > 0, then the angle varies within 0< /4, which corresponds to the "+" sign in the formula. Accordingly, for the left polarization, the sign is "–".
Parameters a,b and can be determined experimentally, and knowing these quantities, the formulas can be used to calculate the amplitudes E 10 ,E 20 and phase difference .
What is a CPL polarizing filter? This is a valuable accessory that any photographer should have in their bag. How does a polarizer affect an image? In order to develop an intuition about this point, it is often necessary to experiment for a long time. In this article, you will learn how to speed up this process, how and how this product can make the task easier (and sometimes harmful) in different situations.
Where is the CPL filter attached? It is always in front of the front. How does this device work? It filters direct reflections of sunlight at certain angles. This is useful, as other light is often richer in hue and more diffuse. Working with this device also requires increasing shutter speed (because some beams are deflected). The filtration angle is controlled by rotating the device. The strength of the effect depends on finding the line of view of the camera relative to the sun.
Filter rotation
When can a CPL filter be used for maximum effect? Only if the camera's line of sight is perpendicular to the sunlight. You can imagine this by pointing your index finger at the sun, while placing your thumb at a right angle to it. As you rotate your hand to point toward the sun, whatever course your thumb points to will determine the line of the polarizer's highest effect.
However, the fact that the CPL filter will provide the best result in these directions does not necessarily mean that it will be most noticeable in them. The limiting polarization will appear during its rotation, which will change the angle relative to the daylight. To get a feel for how the filter works, it's best to rotate it while looking at the camera's display or viewfinder.
An unsuitable result may be obtained during application, since the polarizing effect depends on the angle. One part of the picture can be placed at right angles to the sun, and the other - towards it. In this case, on one side of the photo, the polarization effect will not be noticeable, and on the other side, it can be seen.
Obviously, wide-angle lenses are not perfect. However, the turns of the "polar" can sometimes make the effect more vital. Very often, professionals place the most pronounced polarization action closer to the edge or corner of the image.
Description
Photographers use two types of filters to create high-quality images: linearly polarized and circular. These devices isolate and isolate areas rich in polarized reflected light. With their help, when shooting the bottom, you can weed out bright glare, or capture the landscape outside the window without your own reflection in the glass.
Linear filters perform one simple job - they transmit modified light in a single plane. Devices with circular polarization give access to rays modified in a circle. They turn any refraction of rays into a spherical one. In fact, the circular “polarizer” does not interfere with autofocus, allows you to correctly guess the exposure and can be installed on all cameras (including old ones).
In this case, excessive glare will be eliminated in the same way as in a device with linear polarization. CPL-filter gives a "pure" spherical refraction of light only at a specific wavelength. In a wave plate, the optical difference in its path between the simple and extraordinary rays is exactly a quarter of its length. For all other wavelengths, this device will show an elliptical effect.
Circular filters are more complex than others, so their cost is higher. On the outside of this device there is an ordinary linear device, and on the inside - a quarter-wave plate that turns linear polarization into spherical.
The photo
Polarizing filters for a camera are devices designed to eliminate unwanted effects (reflections, glare), reduce the brightness (with a parallel increase in saturation) of the sky and other objects, to achieve aesthetic goals. They look like ordinary filters, but have front and back parts of equal thickness that can rotate freely.
How is the CPL filter applied? What is this device for? Its back is screwed to the lens, and the desired effect is selected by turning the front half to any angle. The front segment can be equipped with an internal thread, with which an objective cap, threaded hood or other light filters are attached, which is an irrefutable plus.
Different segments of reflective objects can give a reflection with different polarization angles, which cannot be suppressed synchronously by a single filter. In addition, there may be a large number of casting objects in the frame. In such cases, several sequentially twisted polarizing filters are used, and all, except for the rear, must be linearly polarized. This is necessary because the optical compensator placed in the circular filter prevents other devices that may be placed behind it from achieving the effect.
What else is famous for a polarizing filter for a lens? Its usually located in the range of two to five. Color distortion may occur. In general, some devices have a drop of up to one stop in the purple-blue region, which causes the picture to turn out with a green tint. Cheap devices can disgustingly reproduce small details. The Polarik, along with the "protective" UV-blocking filter, is the most exploited device in photography.
Details
Usually a polarizing filter is produced in the form of two plates made of glass. Between them is placed a polaroid film with linear dichroism. This detail is a certain layer of acetylcellulose containing an impressive number of the smallest microlites of herapatite (the iodide compound of quinine sulfate).
Such polyvinyl-iodine films with polymer chains synchronously oriented are used. The orientation of the microlites is identical due to the electric field, and the polymer chains are guided by mechanical tension. The circular filter is also equipped with an optical compensator - a quarter-wave phase plate. With this part, you can determine the difference in the path of the two launches of the beams. It works in accordance with the phenomenon of double refraction of light in crystals.
Light transformation
The simple and exceptional beams have different speeds. Their optical path lengths are also not the same. Therefore, they acquire a travel difference, measured by the thickness of the crystal through which they pass. It is installed along the path of the traveling beam behind the polarizer and rotates during assembly until its oscillation axes coincide with the optical axes.
In this position, the quarter-wave plate converts linearly polarized beams into circularly polarized light (and vice versa), increasing the path difference to 90 degrees. With such features, all "polars" are made. The difference in both price and quality is due to additional layers: protective, anti-reflective, water-repellent.
Appearance
When was the polarizing filter for the lens developed? This product was born from the development of TTL camera automation elements, which, unlike photographic materials, became dependent on innovative exposure to light.
In general, linearly polarized radiation makes it difficult to measure exposure and, in SLR cameras, partially interferes with the operation of automatic phase focusing.
In astronomy, "polarists" are part of the devices with which they study the circular and linear changes in the light of objects in outer space.
Polarization surveillance is the basic method for obtaining information about the strength of the magnetic field in radiation generation regions, say, on white dwarfs.
Nikon CPL
The Nikon 52 mm CPL polarizing filter is a valuable item for landscape photographers and anyone who likes to get high quality shots. There are at least six reasons why you should buy this product:
- For photographing water (it becomes darker and more transparent).
- Shooting a landscape (the “saturation” of greenery and sky increases).
- For shooting at an angle through a window (to eliminate glare and reflections from the glass).
- Elimination of reflections on a sunny day (from water, glass, cars).
- Increase shutter speed by a couple of stops (when needed).
- Protection of the lens from mechanical impact.
Those who go to travel to warm countries need to buy this filter - this is an indispensable assistant in making colorful photos. In bright sunlight, this device improves image quality by increasing contrast and saturation while eliminating haze.
Restrictions
Those people who want to learn how to take good pictures take photography lessons from professionals. How to use a polarizing filter? The device of the desired diameter must be screwed onto the camera lens. By rotating the crystal in the filter, you need to select the desired one, which will allow you to eliminate glare from water or glass when shooting, as well as get more fluffy and white clouds, a saturated sky.
There are some restrictions on the use of such devices:
- When rotating the polarizing filter, it must be taken into account that the expected region of the limiting effect will be located approximately 90 degrees from the primary position. If the device is rotated 180 degrees, this maneuver will return the picture to its initial state.
- "Polars" soften the light flux entering the camera matrix through the lens, so professionals often increase the exposure balance by 1-2 steps.
Flaws
Photography lessons are necessary for beginner photographers to create high-quality pictures. We have found that polarizers are very useful. Unfortunately, they have the following disadvantages:
- Due to this device, the exposure may ask for 4-8 times more light (by 2-3 stops) than usual.
- They need a certain angle in relation to the sun to get the best result.
- With these filters, it is difficult to navigate the camera viewfinder.
- These are one of the most expensive devices.
- They require rotation, so they can increase the composition selection time.
- Usually they cannot be used for wide-angle and panoramic shots.
- If the filter is dirty, it may reduce the quality of the picture.
Moreover, sometimes reflections are needed in a photograph. The most striking examples here are rainbows and sunsets. It is worth applying a polarizer to any of them, colorful reflections can disappear completely or fade.
Camera filters are complex devices. But over time, you can learn to work with them. "Polarik" can sometimes be used when it is necessary to increase the exposure time. Since it can reduce the transmitted light by 4-8 times (2-3 stops), it can be used to shoot water and waterfalls.
If you put a polarizer on a wide-angle lens, it can create a bright darkening of the edges of the picture ("vignetting"). To avoid this, you will probably have to purchase a more “thin” expensive option.
Circular polarizers were designed to keep the camera's autofocus and metering systems working while the filter was in place. Linear "polars" are much cheaper, but they cannot be used with most digital SLR cameras (as they use phase detection autofocus and TTL - metering through the lens).
When considering a plane wave in a homogeneous isotropic medium, it was shown that it is transverse, i.e. the vectors are perpendicular to the propagation direction (axis). For the sake of simplicity, it was assumed that the vector is oriented along the axis, and it was found that in this case the vector is oriented along the axis (figure Figure 50).
−The simplest case of a linearly polarized wave
However, it should be borne in mind that the orientation of the vectors and relative to the coordinate axes depends on the source that creates the wave. In the general case, the directions of the vectors may differ from the direction of the coordinate axes, which means that each of the field vectors may have components along both coordinate axes, and the initial phases of the components may differ. This leads to the fact that the position of the vector in space will differ from the simplest case, when this vector always oscillates in a plane.
The polarization of the electromagnetic wave is the orientation in space of the electric field strength vector .
There are three types of polarization: linear, circular and elliptical. As will be shown, all three of these views are special cases of the general elliptic representation.
Linear polarization
The simplest case is linear polarization. If we consider the expression for the vector:
then it turns out that half of the period the direction of the vector coincides with the positive direction of the axis, and the second half is opposite to it (Figure 51). Thus, at a fixed point in space, the end of the vector moves along a segment of a straight line over time, and the magnitude of the vector changes in the interval. Waves with such a vector orientation are called linearly polarized. The plane passing through the direction of propagation of the wave and the vector is called the plane of polarization. In the example under consideration, the plane of polarization is a plane.
− Electromagnetic wave with linear polarization
Linear polarization is extremely often used in antenna technology. Thus, all local (not satellite) television and radio broadcasting is carried out on radio waves of linear polarization. The position of the plane of polarization is completely determined by the orientation of the receiving and transmitting antennas. Since the plane of linear polarization can be either a plane parallel to the earth's surface or perpendicular to it, they are usually called the horizontal and vertical planes of polarization, respectively. Thus, television broadcasting is usually carried out in the horizontal plane of polarization, and radio broadcasting - in the vertical one, although there are exceptions.
Superposition of two linearly polarized waves
Let us now assume that the wave is created by a more complex radiating structure and the vector has two components, which change either in phase or with some phase shift. The vector in this case also has two components associated with the components. Then, in the general case, the expression for the vector of a plane wave in a lossless medium can be written as
where and are the amplitudes of the components and, respectively, and ai are the phases of these components at the point at. A wave of this type can be considered as a superposition of two linearly polarized plane waves with mutually perpendicular polarization planes propagating in the same direction along the axis. The nature of the change in the vector over time at a fixed point in space depends on the ratio between the initial phases, and on the amplitudes.
Let us consider what happens in individual special cases of such a wave. To do this, consider the angle between the axis and the vector at some fixed point in space. Obviously, the value of this angle depends on the ratio between the instantaneous values of the vector components (figure Figure 52):
that is, depends on the ratio of quantities, and, and generally changes with time. To obtain the case of linear polarization, it is necessary that the components of the vector be in-phase or anti-phase. Let's put it first, then
In this case, the vector at any time lies in a plane passing through the axes making an angle with the plane.
−Linearly polarized wave
A similar phenomenon also occurs when the difference between the initial phases is equal to an integer:
Obviously, at or linearly polarized wave turns into a wave with a purely horizontal or purely vertical polarization.
− Horizontal and vertical polarization
Let's consider the second special case. Let the amplitudes of the components be equal, and the initial phases differ by:
Substituting these values into the expression for the angle , we get:
whence it follows that
where is an integer. This equality means that the angle at a fixed point in space increases with time. The value of the vector remains unchanged:
Thus, at a fixed point in space, the vector , remaining unchanged in magnitude, rotates with an angular frequency around the direction of the axis. In this case, the end of the vector describes a circle (figure Figure 54). Waves of this type are called circularly polarized waves.
−Circular polarization of a plane wave
It is also easy to verify that the wave will have circular polarization not only in the case , but also
Along the direction of propagation (along the axis ) at a fixed point in time in a lossless medium, the end of the vector describes a helix with a step equal to the wavelength. The projection of this line onto a plane forms a circle. Over time, this helical line moves along the axis along the cylinder with phase velocity.
Depending on the direction of rotation of the vector around the axis of propagation, waves with left and right circular polarization are distinguished. In the case of right-hand polarization, the vector rotates clockwise if viewed along the direction of propagation, and in the case of left-hand circular polarization, it rotates counterclockwise. In the considered example, the wave has right-hand polarization. Obviously, the same polarization will be in the case
the wave has left-hand circular polarization.
The vector of a homogeneous wave is everywhere and at any moment of time perpendicular to the vector and proportional to it in magnitude. Thus, in contrast to linear polarization, the field of a traveling wave with circular polarization at any point in time is not equal to zero at any point in space.
In the case of a lossy medium, the line connecting the ends of the vectors at the same time at different points on the axis is a spiral with a radius that varies along the axis according to the law.
In the most general case of wave propagation, when the end of the vector will describe an ellipse in fixed and variable space (Figure 55). The semiaxes of an ellipse generally do not coincide with the coordinate axes.
−Elliptically polarized wave
To determine the ellipticity of the field, the ellipticity coefficient is used, which characterizes the ratio of the minor semiaxis of the ellipse to the major one:
When the ellipse degenerates into a circle, this case corresponds to an electromagnetic wave with circular polarization. If, then the ellipse degenerates into a straight line - this is a linearly polarized wave.
When considering elliptical and circular polarizations, we considered the superposition of two linearly polarized waves. As we have seen, a field with any type of polarization can be represented as a sum of two waves polarized linearly in two orthogonal planes. The converse can also be proven: an elliptically or linearly polarized wave can be represented as the sum of two waves with circular polarization and opposite directions of rotation.
Let in the direction of the axis oz two electromagnetic waves propagate. The electric field strength of one wave oscillates in the direction of the axis OY in law EY(z, t)= Eosin(kz-wt), and the other - in the direction of the axis OX in law Ex(z, t)= Eocos(kz-wt).Phase of oscillations of a wave with an electric field oriented along the axis OX, lags behind p/2 from the phase of another wave. Let us find out the nature of the oscillations of the intensity vector of the resulting wave.
One can simply make sure that the modulus of the resulting wave does not change with time and is always equal to Eo. The tangent of the angle between the axis OX and the electric field strength vector at the point z equals
tgj===tg(kz-wt). (one)
From (1) it follows that the angle between the electric field vector of the wave and the axis OX-j- changes over time j(t)=kz-wt.The electric field strength vector rotates uniformly with an angular velocity equal to w. The end of the electric field strength vector moves along a helix (see Figure 27). If we look at the change in the intensity vector from the origin in the direction of wave propagation, then the rotation occurs clockwise, i.e. in the direction of the magnetic induction vector. Such a wave is called right circularly polarized.
An electromagnetic wave with circular polarization, incident on a substance, transfers rotation to the electrons of the substance.
Outcome: right polarized an electromagnetic wave has an angular momentum directed along the propagation of the wave, left polarized An electromagnetic wave has an angular momentum directed against the propagation of the wave. This result will be used in the study of quantum physics.
When adding plane waves of linear polarization with planes oriented at a right angle and with an arbitrary phase shift a, the resulting change in the intensity vector at a given point z can be a rotation with a simultaneous periodic change in the modulus. The end of the electric field vector of the wave in this case moves along an ellipse. This type of polarization is called elliptical. It can be either left or right. Figure 29 shows the trajectories of the end of the vector of the resulting electric field of two waves of the same amplitude with horizontal and vertical polarization planes for different values of the phase shift - from 0 before p. With a phase shift equal to zero, the resulting wave is plane polarized with the plane of polarization making an angle p/4 with a horizontal plane. With a phase shift equal to p/4, is the elliptical polarization, with p/2– circular polarization, at 3p/4– elliptical polarization, at p- linear polarization.
In the case when the wave is a sum of randomly polarized components with a chaotic set of phase shifts, all polarization effects are lost. It is said that the electromagnetic wave in this case is not polarized.
